# Justice, Inferential Statistics and Lucia de Berk

Students of inferential statistics are very fond of “p value”. A null hypothesis is either rejected or not rejected based on p value. If p value is lower than accepted level of significance then null hypothesis gets rejected.

But this small number can create lot of havoc- in case of Lucia de Berk it turned her life upside down.

Lucia de Berk was a paediatric nurse who worked at hospital in Hague. It was her third job, prior to this she had worked in two other hospitals. One day when she was on duty a child called Amber died. This led to investigation and it was found that there were 8 more such cases when she was on duty, so 9 cases of death in 3 hospitals.

During prosecution, Henk Elffers was used by courts as statistics expert. Based on data collected from hospitals he calculated p value for each hospital, and then did meta-analysis by multiplying p values, to arrive at grand p value. This method of calculating composite value by simply multiplying p values is not correct; there is method for  that- Fisher method.

Henk Elffers method of calculation was not just incorrect, but also hilarious. P values are very small values, generally p value less than .05 is considered to be statically significant.. Now let us assume that p value for each case is .06 i.e not statistically significant, now if Lucia worked for 3 hospitals then p value as per Henk’s method is .06x.06x.06= .0002 i.e. highly significant. Now if Lucia has worked in 10 hospitals, we would end up with ridiculously low p value- .06^10.

Based on his wrong calculations, Henk concluded that chance of a nurse working at the three hospitals being present at the scene of so many unexplained deaths is one in 342 million, which was equated with chances of her being innocent.

Based on these calculations Lucia was declared guilty and sentenced with life imprisonment.

Later case went to higher court and all statistical evidence against Lucia was dismissed and Lucia was set free. A film was made on her called Lucia de B.

So next time when you accept or reject null hypothesis based on p value, think of impact this small number can create.